He said talks with Mr Kim on Wednesday had been "warm", "constructive", and "good" and he made clear if North Korea gets rid of its nuclear weapons in a permanent and verifiable way, the U.S. is willing to help the impoverished nation boost its economy and living stands to levels like those in prosperous South Korea.

Abe also said worldwide sanctions should remain in place against North Korea and any rewards must wait until Kim fully abandons his nuclear and missile programs.

She also said there must be "airtight" coordination between South Korea and the USA ahead of Donald Trump and Kim Jong Un historic meeting on 12 June.

"We had good conversations about the histories of our two nations, the challenges that we have had between us", Mr Pompeo told reporters at a news conference with South Korea's visiting foreign minister Kang Kyung-wha.

"We are bewildered by the incessant calls of the United States and their allies 'to continue to increase pressure on North Korea" even while Pyongyang shows readiness for a constructive dialogue on the Korean crisis settlement", the ministry said in a statement.

Pompeo said there would need to be "complete" and "verifiable" denuclearization, suggesting it would involve inspections to ensure the North's compliance.

Japan says North Korea abducted at least 17 Japanese citizens in the 1970s and 1980s to train agents in Japanese culture and language to spy on South Korea.

But he added: "I'm confident that we have a shared understanding of the outcome that the leaders want, certainly President Trump and chairman Kim, but I think President Moon as well".

"If Chairman Kim chooses the right path, there is a future brimming with peace and prosperity for the North Korean people", he said.

So far, the North Korean regime has made vague pledges to "denuclearize" but has not spelled out what that means, when it would happen or how it would be implemented. "I hope Mr. Trump will make a breakthrough to achieve our goals".

In North Korea's bombastic rhetoric, "denuclearization" has, for years, been a byword for USA troop withdrawals from South Korea - an idea that Kang appeared to reject.

Amid concerns that North Korea will demand the US withdraw its troops from neighbouring South Korea, Ms Kang emphasised that the US military presence there must be "a matter for the US-ROK alliance first and foremost", using an acronym for South Korea's official name, the Republic of Korea.

Hardliners in the North are believed to see a nuclear weapon as a guarantee against outside efforts to topple the regime, but Trump insists he will not tolerate their growing arsenal.